Question
Asked Feb 4, 2020
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4. The Poisson distribution is an important discrete distribution used to model events that occur
with characteristic rates. It is also the underlying statistical model for regression techniques
involving categorical data. The pmf of the Poisson distribution is given by:
ake-2
P(X = k)
k!
a) Show that the mean/expected value of this distribution is given by:
E(X) = 1
b) Show that the variance of this distribution is given by:
Var(X) = E(X²) – (E(X))² = 1
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4. The Poisson distribution is an important discrete distribution used to model events that occur with characteristic rates. It is also the underlying statistical model for regression techniques involving categorical data. The pmf of the Poisson distribution is given by: ake-2 P(X = k) k! a) Show that the mean/expected value of this distribution is given by: E(X) = 1 b) Show that the variance of this distribution is given by: Var(X) = E(X²) – (E(X))² = 1

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Step 1

a) Expected value:

The expected value is given below:

Probability homework question answer, step 1, image 1
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Step 2

b.

The variance is calculated by th...

Probability homework question answer, step 2, image 1
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